Cox Proportional Hazards Model
Halley Deleeuw and Jasmine Sawh
2023-11-30
Introduction to Cox Proportional Hazards Model
Developed by Sir David R. Cox in 1972
Statistical method for survival analysis and epidemiological research
Analyzes time-to-event data
Estimates hazard function
Explores relationships with independent variables
Applications include healthcare, engineering, social sciences
Methods
Semiparametric survival analysis method
Right-censored data
\[ λ(t) = λ0(t) * exp(β₁X₁ + β₂X₂ + ... + βₖ) \]
Assumptions/Limitations
Proportional Hazard Assumption
Linearity of Continuous Variables
Independence of Censoring
Sensitivity to Outliers
Data Description
National Cancer Institute Surveillance, Epidemiology, and End Results Program (SEER)
Comprehensive cancer surveillance system in the US
Covers a wide range of demographic information
Provides insights into cancer trends, outcomes, and risk factors at a national level
Data Table
Data Visualization
Patient Age
Patients Race
Patients Gender
Patients Origin
Year of Diagnosis
Survival
Cancers
Alive Patients
Deceased Patients
Median Income
Objective and Purpose
Explore factors impacting patient survival
Analyze key variables such as cancer type, race, gender, age
Understanding their significance in predicting survival
Assess hazard ratios for each variable
Center analysis on relationships and impact on survival outcomes
Statistical Modeling for Data
Results
Residuals
QQPlot
SR Cancer
SR Race
SR Gender
SR Age
Stratified Analysis
Results
Residuals
QQPlot
SR Race
SR Gender
SR Age
Adding an Interaction term to Filtered Analysis on Deceased Patients
Results
Residuals
QQPlot
SR Gender
SR Cancer
SR Gender:Cancer
Data Analysis with Reference Categories
Results
Residuals
QQPlot
SR Age
SR Gender
SR Race
Model with Time-Dependent Covariates
Results
Residuals
QQPlot
Conclusion
Identified key predictors impacting cancer survival
Explored survival dynamics
Proportional Hazards assumption violated
Stratification, Interaction Term, Time-Dependent covariates
References